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Mathematics 2019, 7(2), 204; https://doi.org/10.3390/math7020204

On the Domain of the Fibonacci Difference Matrix

1
Kilis Yatırım Destek Ofisi, Şehitler Mah. Cambazlar Sok. No:9, Kilis 79000, Turkey
2
Faculty of Arts and Sciences, Department of Mathematics, Gaziantep University, Gaziantep 27310, Turkey
*
Author to whom correspondence should be addressed.
Received: 31 December 2018 / Revised: 17 February 2019 / Accepted: 19 February 2019 / Published: 21 February 2019
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Abstract

Matrix F^ derived from the Fibonacci sequence was first introduced by Kara (2013) and the spaces lp(F) and l(F); (1 ≤ p < ∞) were examined. Then, Başarır et al. (2015) defined the spaces c0(F) and c(F) and Candan (2015) examined the spaces c(F(r,s)) and c0(F(r,s)). Later, Yaşar and Kayaduman (2018) defined and studied the spaces cs(F(s,r)) and bs(F(s,r)). In this study, we built the spaces cs(F) and bs(F). They are the domain of the matrix F on cs and bs, where F is a triangular matrix defined by Fibonacci Numbers. Some topological and algebraic properties, isomorphism, inclusion relations and norms, which are defined over them are examined. It is proven that cs(F) and bs(F) are Banach spaces. It is determined that they have the γ, β, α -duals. In addition, the Schauder base of the space cs(F) are calculated. Finally, a number of matrix transformations of these spaces are found. View Full-Text
Keywords: matrix transformations; Fibonacci numbers; sequence spaces; Fibonacci double band matrix; γ, β, α -duals matrix transformations; Fibonacci numbers; sequence spaces; Fibonacci double band matrix; γ, β, α -duals
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Yaşar, F.; Kayaduman, K. On the Domain of the Fibonacci Difference Matrix. Mathematics 2019, 7, 204.

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